The equation of state for metal-doped ferroelectrics within the Weiss model

Abstract

This paper presents a theoretical model for describing the thermodynamic properties of doped ferroelectric crystals based on a modified Weiss mean-field approach. Accounting for quadrupole and octupole terms in the expression for the effective field within the Weiss model makes it possible to move from the Langevin equation to the Landau–Ginzburg equation. Furthermore, the coefficients of the Landau–Ginzburg equation can be expressed in terms of the physical parameters of the crystal lattice. For these parameters, analytical expressions are proposed that describe their change when adding dopants in ceramic matrix composites. Perovskite barium titanate ceramics with a variety of inclusions is considered as an application example of the developed method. The obtained agreement between the analytical and experimental results for barium titanate ceramics with lanthanum/magnesium/zirconium dopants gives us hope of the applicability of the present theory to the calculation of other doped ferroelectrics as well.